Here is an interesting set of connections between reaction diffusion systems in chemistry, simulations based on differential equations to model those reactions and discrete cellular automata that have nothing to do with either of those!
(trying to put this story together)
The most famous reaction diffusion equation is the Belousov Zhabotinsky reaction where you mix 5 chemicals together in a homogenous solution. The reaction is powered by the Bromine containing molecules oxidizing an organic compound. Those 5 initial chemicals interact with each other to produce a network of dozens of chemicals that amplify microscopic fluctuations in the homogenous space and eventually create spriral structures that move across the medium. Very cool.
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https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXRy4biunmvQ_Uj1dYv6QBaSL0d-3cEcxVYBdwyGIsjaKEMe1rUHM1xQJgtFBJkhWz7O5KTnewLBe_MsoFupGueMcsV0X8B4_ThhW-a8bnEpF7lttn0RdK0G3PFdX1hcFWMB7l_DvMGAWu/s1600/chemical_physical_reactions_12.gif
[ref]
https://www.faidherbe.org/site/cours/dupuis/oscil.htm
A related chemical system is CIMA: Chlorite, Iodide, and Malonic Acid. This reaction was later shown to be an example of a reaction imagined by Alan Turing when he was trying to figure out how stripes could spontaneously occur in animal development.
references below.
Then Swinney and Pearson worked on the mathematics and related chemical reactions and got a chemical system of replicating moving spots.
[do i have a video?]
i found one video of a system with parameters that look close to replicating spots
https://www.youtube.com/watch?v=JBvKuLS78js
by Tomonago Ueno
(Is this like the grey scott mechanism?) it's triggered by ultraviolet light in ferrocyanide iodate sulphite
K. -J. Lee, W. D. McCormick, J. E. Pearson and H. L. Swinney 94 Experimental observation of self -replicatin spots in a reaction -diffusion system Nature 369 (1994) p215-218 PDF at chaos.ph.utexas.edu: lee et al (link at munafo uskate)
Pearson first saw these replicating spots on computer simulation of reaction diffusion. IS HE THE FIRST ONE TO FIND THIS BEHAVIOR IN GRAY SCOTT?
Pearson, Complex patterns in a simple system, Science 261 (1993) p189-192 (arXiv.org: patt-sol/9304003
K. J. Lee, W. D. McCormick, Q. Ouyang, and H. L. Swinney, Pattern formation by intercting chemical fronts, Science 261 (1993) 192-194
K. J. Lee, W. D. McCormick, H. L. Swinney, and J. E. Pearson, Experimental observation of self-replicating spots
another
Kyoung J. Lee and Harry L. Swinney
Replicating Spots in Reaction-Diffusion Systems
International Journal of Bifurcation and Chaos VOL. 07, NO. 05
Abstract
We review the phenomenon of replicating spots in reaction-diffusion systems and discuss the mechanism of replication. This phenomenon was discovered in recent experiments on a ferrocyanide-iodate-sulfite reaction-diffusion system. Patterns form in a thin gel layer that is in contact with a continuously fed stirred reservoir. Patterns of spots are observed to undergo a continuous process of growth and multiplication through cell division and death through overcrowding. A similar phenomenon is also found in numerical simulations in one dimension on a four-species model of the ferrocyanide-iodate-sulfite reaction and in simulations in two dimensions of simpler two-species reaction-diffusion models: Gray–Scott model by J. Pearson and FitzHugh–Nagumo model by A. Hagberg and E. Meron.
J. Boissonade, E. Dulos and P. De Kepper (95) "Turing patterns: from myth to reality" in Chemical waves and patterns (ed R Kapral and K showalter. Klewer.
1) there is Evans larger than life, larger and larger neighborhoods
ok chapter 11 in my adamatzky life book 43pages of details.
Griffeath first invents larger than life family to see if gol is a phase transition between periodic and nonperiodic 94
Griffeath, D.: Self-organization of random cellular automata: four snapshots. In: Grimmett, G. (ed.) Probability and Phase Transitions, pp. 49–67. Kluwer Academic, Dordrecht/Norwell
(1994)
then k. evans explores
Evans, K.: Larger than Life: it’s so nonlinear. Ph.D. Dissertation, University of Wisconsin–Madison (1996).
http://www.csun.edu/~kme52026/thesis.html
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2005 discovers bosco which looks like uskates
Evans, K.: Is Bosco’s rule universal? In: Margenstern, M. (ed.) Machines, Computations, and Universality. Lecture Notes in Computer Science, vol. 3354, pp. 188–199. Springer, Berlin
(2005). WWW companion page to paper:
http://www.csun.edu/~kme52026/bosco/bosco.html
MORE ON CIMA
Patrick de Kepper et al u. bordeaux first got turing reaction: chlorite and iodide ions and malonic acid in thin layer of gell that was ontinuously fed from opposite directions with fresh reagents. bands appear in the middle. under the right conditions, the bands break up into discrete dots. did this in early 80s as alternative to bz. called CIMA
put in starch to see color binding to tri-iodide ions.
the chlorite is the inhibitor and it diffuses fast, the iodide is the activator and it gets slowed down by the starch/gel
close to bz but closer to turing, has activator iodide and inhibitor chlorite
irving epstein in 91 did mathematical analysis showing it's turing pattern
Q. Quyang and h.l. swinney 91 ttransition from a uniform state to hexagonal and striped turing patterns" nature 352, 610
then got the pttern to form over larger areas. and got phase transition from homogenous to spots by lowering the temp (melting the gel) and got tx from stripes to spots by changing concentrations
q. quyang and h. l. swinney 95 onset and beyond turing pattern formation in
r. kapral and k. showalter eds 95 chemical waves and patterns kluwer acad pubs
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